This paper presents a new concept flexure hinge for MEMS applications and reveals how to design, construct, and experimentally test. This hinge combines a curved beam, as a flexible element, and a pair of conjugate surfaces, whose contact depends on load conditions. The geometry is conceived in such a way that minimum stress conditions are maintained within the flexible beam. A comparison of the new design with the other kind of revolute and flexible joints is presented. Then, the static behavior of the hinge is analyzed by means of a theoretical approach, based on continuum mechanics, and the results are compared to those obtained by means of finite element analysis (FEA) simulation. A silicon hinge prototype is also presented and the construction process, based on single step lithography and reactive ion etching (RIE) technology, is discussed. Finally, a crucial in–SEM experiment is performed and the experimental results are interpreted through the theoretical models.

References

References
1.
Wang
,
D.
,
Yang
,
Q.
, and
Dong
,
H.
,
2013
, “
A Monolithic Compliant Piezoelectric-Driven Microgripper: Design, Modeling, and Testing
,”
IEEE/ASME Trans. Mech.
,
18
(
1
), pp.
138
147
.10.1109/TMECH.2011.2163200
2.
Belfiore
,
N. P.
,
Verotti
,
M.
,
Crescenzi
,
R.
, and
Balucani
,
M.
,
2013
, “
Design, Optimization and Construction of MEMS Based Micro Grippers for Cell Manipulation
,”
IEEE International Conference on System Science and Engineering
, ICSSE 2013,
IEEE
, Budapest, Hungary, July 4–6, pp.
105
110
.10.1109/ICSSE.2013.6614642
3.
Yi
,
B.-J.
,
Chung
,
G. B.
,
Na
,
H. Y.
,
Kim
,
W. K.
, and
Suh
,
I. H.
,
2003
, “
Design and Experiment of a 3-DOF Parallel Micromechanism Utilizing Flexure Hinges
,”
IEEE Trans. Rob. Autom.
,
19
(
4
), pp.
604
612
.10.1109/TRA.2003.814511
4.
Tian
,
Y.
, and
Shirinzadeh
,
B.
,
2009
, “
Development of a Flexure-Based 3-RRR Parallel Mechanism for Nano-Manipulation
,”
IEEE/ASME International Conference on Advanced Intelligent Mechatronics
, Singapore, July 14–17, AIM 2009,
IEEE
, July 4–6, pp.
1324
1329
.10.1109/AIM.2009.5229872
5.
Belfiore
,
N. P.
,
EmamiMeibodi
,
M.
,
Verotti
,
M.
,
Crescenzi
,
R.
,
Balucani
,
M.
, and
Nenzi
,
P.
,
2013
, “
Kinetostatic Optimization of a MEMS Based Compliant 3 DOF Plane Parallel Platform
,”
IEEE 9th International Conference on Computational Cybernetics
, ICCC 2013,
IEEE
, Tihany, Hungary, July 8–10, pp.
261
266
.10.1109/ICCCyb.2013.6617600
6.
Bashash
,
S.
, and
Jalili
,
N.
,
2009
, “
Robust Adaptive Control of Coupled Parallel Piezo-Flexural Nanopositioning Stages
,”
IEEE/ASME Trans. Mech.
,
14
(
1
), pp.
11
20
.10.1109/TMECH.2008.2006501
7.
Polit
,
S.
, and
Dong
,
J.
,
2011
, “
Development of a High-Bandwidth XY Nanopositioning Stage for High-Rate Micro-Nanomanufacturing
,”
IEEE/ASME Trans. Mech.
,
16
(
4
), pp.
724
733
.10.1109/TMECH.2010.2052107
8.
Xu
,
Q.
,
2012
, “
Design and Development of a Flexure-Based Dual-Stage Nanopositioning System With Minimum Interference Behavior
,”
IEEE Trans. Autom. Sci. Eng.
,
9
(
3
), pp.
554
563
.10.1109/TASE.2012.2198918
9.
Howell
,
L.
,
2001
,
Compliant Mechanisms
,
Wiley-Interscience
, New York.
10.
Lobontiu
,
N.
,
2010
,
Compliant Mechanisms: Design of Flexure Hinges
,
CRC
, Boca Raton, FL.
11.
Pei
,
X.
,
Yu
,
J.
,
Zong
,
G.
,
Bi
,
S.
, and
Su
,
H.
,
2009
, “
The Modeling of Cartwheel Flexural Hinges
,”
Mech. Mach. Theory
,
44
(
10
), pp.
1900
1909
.10.1016/j.mechmachtheory.2009.04.006
12.
Cannon
,
J.
, and
Howell
,
L.
,
2005
, “
A Compliant Contact-Aided Revolute Joint
,”
Mech. Mach. Theory
,
40
(
11
), pp.
1273
1293
.10.1016/j.mechmachtheory.2005.01.011
13.
Bellouard
,
Y.
,
2010
,
Microrobotics: Methods and Applications
,
CRC
, Boca Raton, FL.
14.
Bazaz
,
S. A.
,
Khan
,
F.
, and
Shakoor
,
R. I.
,
2011
, “
Design, Simulation and Testing of Electrostatic SOI Mumps Based Microgripper Integrated With Capacitive Contact Sensor
,”
Sens. Actuators, A
,
167
(
1
), pp.
44
53
.10.1016/j.sna.2010.12.003
15.
Beyeler
,
F.
,
Neild
,
A.
,
Oberti
,
S.
,
Bell
,
D.
,
Sun
,
Y.
,
Dual
,
J.
, and
Nelson
,
B.
,
2007
, “
Monolithically Fabricated Microgripper With Integrated Force Sensor for Manipulating Microobjects and Biological Cells Aligned in an Ultrasonic Field
,”
J. Microelectromech. Syst.
,
16
(
1
), pp.
7
15
.10.1109/JMEMS.2006.885853
16.
Chen
,
G.-M.
,
Jia
,
J.-Y.
, and
Li
,
Z.-W.
,
2005
, “
On Hybrid Flexure Hinges
,”
Proceedings on Networking, Sensing and Control
,
IEEE
, Tucson, AZ, Mar. 19–22, pp.
700
704
.10.1109/ICNSC.2005.1461275
17.
Lee
,
V.
,
Gibert
,
J.
, and
Ziegert
,
J.
,
2013
, “
Hybrid Bi-Directional Flexure Joint
,”
Precis. Eng.
,
38
(
2
), pp.
270
278
.10.1016/j.precisioneng.2013.10.001
18.
Yong
,
Y. K.
,
Lu
,
T.-F.
, and
Handley
,
D. C.
,
2008
, “
Review of Circular Flexure Hinge Design Equations and Derivation of Empirical Formulations
,”
Precis. Eng.
,
32
(
2
), pp.
63
70
.10.1016/j.precisioneng.2007.05.002
19.
Lobontiu
,
N.
,
Garcia
,
E.
,
Goldfarb
,
M.
, and
Paine
,
J. S.
,
2001
, “
Corner-Filleted Flexure Hinges
,”
ASME J. Mech. Des.
,
123
(
3
), pp.
346
352
.10.1115/1.1372190
20.
Lobontiu
,
N.
,
Paine
,
J. S.
,
O'Malley
,
E.
, and
Samuelson
,
M.
,
2002
, “
Parabolic and Hyperbolic Flexure Hinges: Flexibility, Motion Precision and Stress Characterization Based on Compliance Closed-Form Equations
,”
Precis. Eng.
,
26
(
2
), pp.
183
192
.10.1016/S0141-6359(01)00108-8
21.
Smith
,
S. T.
,
Badami
,
V. G.
,
Dale
,
J. S.
, and
Xu
,
Y.
,
1997
, “
Elliptical Flexure Hinges
,”
Rev. Sci. Instrum.
,
68
(
3
), pp.
1474
1483
.10.1063/1.1147635
22.
Xu
,
P.
,
Jingjun
,
Y.
,
Guanghua
,
Z.
, and
Shusheng
,
B.
,
2008
, “
The Stiffness Model of Leaf-Type Isosceles-Trapezoidal Flexural Pivots
,”
ASME J. Mech. Des.
,
130
(
8
), p.
082303
.10.1115/1.2936902
23.
Zhang
,
S.
, and
Fasse
,
E.
,
2001
, “
A Finite-Element-Based Method to Determine the Spatial Stiffness Properties of a Notch Hinge
,”
ASME J. Mech. Des.
,
123
(
1
), pp.
141
147
.10.1115/1.1342157
24.
Chen
,
G.
,
Liu
,
X.
, and
Du
,
Y.
,
2011
, “
Elliptical-Arc-Fillet Flexure Hinges: Toward a Generalized Model for Commonly Used Flexure Hinges
,”
ASME J. Mech. Des.
,
133
(
8
), p.
081002
.10.1115/1.4004441
25.
Lobontiu
,
N.
,
2012
, “
Symmetry-Based Compliance Model of Multisegment Notch Flexure Hinges
,”
Mech. Based Des. Struct. Mach.
,
40
(
2
), pp.
185
205
.10.1080/15397734.2011.629166
26.
Chen
,
G.
,
Wang
,
J.
, and
Liu
,
X.
,
2014
, “
Generalized Equations for Estimating Stress Concentration Factors of Various Notch Flexure Hinges
,”
ASME J. Mech. Des.
,
136
(
3
), p.
031009
.10.1115/1.4026265
27.
Zelenika
,
S.
,
Munteanu
,
M.
, and
De Bona
,
F.
,
2009
, “
Optimized Flexural Hinge Shapes for Microsystems and High-Precision Applications
,”
Mech. Mach. Theory
,
44
(
10
), pp.
1826
1839
.10.1016/j.mechmachtheory.2009.03.007
28.
Dirksen
,
F.
,
Anselmann
,
M.
,
Zohdi
,
T.
, and
Lammering
,
R.
,
2013
, “
Incorporation of Flexural Hinge Fatigue-Life Cycle Criteria Into the Topological Design of Compliant Small-Scale Devices
,”
Precis. Eng.
,
37
(
3
), pp.
531
541
.10.1016/j.precisioneng.2012.12.005
29.
Jensen
,
B.
, and
Howell
,
L.
,
2002
, “
The Modeling of Cross-Axis Flexural Pivots
,”
Mech. Mach. Theory
,
37
(
5
), pp.
461
476
.10.1016/S0094-114X(02)00007-1
30.
Shusheng
,
B.
,
Hongzhe
,
Z.
, and
Jingjun
,
Y.
,
2009
, “
Modeling of a Cartwheel Flexural Pivot
,”
ASME J. Mech. Des.
,
131
(
6
), p.
061010
.10.1115/1.3125204
31.
Mankame
,
N. D.
, and
Ananthasuresh
,
G.
,
2004
, “
Topology Optimization for Synthesis of Contact-Aided Compliant Mechanisms Using Regularized Contact Modeling
,”
Comput. Struct.
,
82
(
15
), pp.
1267
1290
.10.1016/j.compstruc.2004.02.024
32.
Belfiore
,
N. P.
, and
Simeone
,
P.
,
2013
, “
Inverse Kinetostatic Analysis of Compliant Four-Bar Linkages
,”
Mech. Mach. Theory
,
69
, pp.
350
372
.10.1016/j.mechmachtheory.2013.06.008
33.
Yong
,
Y. K.
, and
Lu
,
T.-F.
,
2008
, “
The Effect of the Accuracies of Flexure Hinge Equations on the Output Compliances of Planar Micro-Motion Stages
,”
Mech. Mach. Theory
,
43
(
3
), pp.
347
363
.10.1016/j.mechmachtheory.2007.03.007
34.
Belfiore
,
N. P.
,
Scaccia
,
M.
,
Ianniello
,
F.
, and
Presta
,
M.
,
2009
,
Selective Compliance Hinge
, WO/2009/034551, International Application No. PCT/IB2008/053697, Mar. 19.
35.
Belfiore
,
N.
,
Scaccia
,
M.
,
Ianniello
,
F.
, and
Presta
,
M. P. L.
,
2009
,
Selective Compliance Wire Actuated Mobile Platform, Particularly for Endoscopiy Surgical Devices
, WO/2009/034552, International Application No. PCT/IB2008/053698, Mar. 19.
36.
Cullmann
,
K.
,
1880
,
Traite de Statique Graphique
, Dunod, ed.,
Paris
.
37.
Ferrari
,
R.
, and
Rizzi
,
E.
,
2008
, “
On the Theory of the Ellipse of Elasticity as a Natural Discretisation Method in the Design of Paderno d'adda Bridge (Italy)
,”
Proceedings of the 6th International Conference on Structural Analysis of Historic Construction: Preserving Safety and Significance
, Bath, UK, July 2–4, CRC, pp.
583
591
.
38.
Tas
,
N.
,
Sonnenberg
,
T.
,
Jansen
,
H.
,
Legtenberg
,
R.
, and
Elwenspoek
,
M.
,
1996
, “
Stiction in Surface Micromachining
,”
J. Micromech. Microeng.
,
6
(
4
), p.
385
.10.1088/0960-1317/6/4/005
39.
Komvopoulos
,
K.
,
1996
, “
Surface Engineering and Microtribology for Microelectromechanical Systems
,”
Wear
,
200
(
1
), pp.
305
327
.10.1016/S0043-1648(96)07328-0
40.
Mastrangelo
,
C.
,
1997
, “
Adhesion-Related Failure Mechanisms in Micromechanical Devices
,”
Tribol. Lett.
,
3
(
3
), pp.
223
238
.10.1023/A:1019133222401
41.
Maboudian
,
R.
, and
Howe
,
R. T.
,
1997
, “
Critical Review: Adhesion in Surface Micromechanical Structures
,”
J. Vac. Sci. Technol., B
,
15
(
1
), pp.
1
20
.10.1116/1.589247
42.
Rymuza
,
Z.
,
1999
, “
Control Tribological and Mechanical Properties of MEMS Surfaces. Part 1: Critical Review
,”
Microsyst. Technol.
,
5
(
4
), pp.
173
180
.10.1007/s005420050160
43.
Ashurst
,
W. R.
,
Yau
,
C.
,
Carraro
,
C.
,
Maboudian
,
R.
, and
Dugger
,
M. T.
,
2001
, “
Dichlorodimethylsilane as an Anti-Stiction Monolayer for MEMS: A Comparison to the Octadecyltrichlorosilane Self-Assembled Monolayer
,”
J. Microelectromech. Syst.
,
10
(
1
), pp.
41
49
.10.1109/84.911090
44.
Ashurst
,
W. R.
,
Yau
,
C.
,
Carraro
,
C.
,
Lee
,
C.
,
Kluth
,
G. J.
,
Howe
,
R. T.
, and
Maboudian
,
R.
,
2001
, “
Alkene Based Monolayer Films as Anti-Stiction Coatings for Polysilicon MEMS
,”
Sens. Actuators, A
,
91
(
3
), pp.
239
248
.10.1016/S0924-4247(01)00593-3
45.
van Spengen
,
W. M.
,
Wijts
,
G. H. C. J.
,
Turq
,
V.
, and
Frenken
,
J. W. M.
,
2010
, “
Microscale Friction Reduction by Normal Force Modulation in MEMS
,”
J. Adhes. Sci. Technol.
,
24
(
15–16
), pp.
2669
2680
.10.1163/016942410X508226
46.
Belfiore
,
N.
,
Verotti
,
M.
, and
Consorti
,
L.
,
2010
, “
Comparative Analysis of Isotropy Indices in RR and RRP Arms
,”
Int. J. Mech. Control
,
11
(
1
), pp.
3
12
.
47.
Belfiore
,
N.
,
Di Giamberardino
,
P.
,
Rudas
,
I.
, and
Verotti
,
M.
,
2011
, “
Isotropy in Any RR Planar Dyad Under Active Joint Stiffness Regulation
,”
Int. J. Mech. Control
,
12
(
1
), pp.
75
81
.
48.
Belfiore
,
N. P.
,
Verotti
,
M.
,
Di Giamberardino
,
P.
, and
Rudas
,
I. J.
,
2012
, “
Active Joint Stiffness Regulation to Achieve Isotropic Compliance in the Euclidean Space
,”
J. Mech. Rob.
,
4
(
4
), p.
041010
.10.1115/1.4007307
49.
Petersen
,
K. E.
,
1982
, “
Silicon as a Mechanical Material
,”
Proc. IEEE
,
70
(
5
), pp.
420
457
.10.1109/PROC.1982.12331
50.
Hopcroft
,
M. A.
,
Nix
,
W. D.
, and
Kenny
,
T. W.
,
2010
, “
What Is the Young's Modulus of Silicon?
,”
J. Microelectromech. Syst.
,
19
(
2
), pp.
229
238
.10.1109/JMEMS.2009.2039697
51.
Kota
,
S.
,
Joo
,
J.
,
Li
,
Z.
,
Rodgers
,
S.
, and
Sniegowski
,
J.
,
2001
, “
Design of Compliant Mechanisms: Applications to MEMS
,”
Analog Integr. Circuits Signal Process.
,
29
(
1
), pp.
7
15
.10.1023/A:1011265810471
52.
Howell
,
L.
,
Midha
,
A.
, and
Norton
,
T.
,
1996
, “
Evaluation of Equivalent Spring Stiffness for Use in a Pseudo-Rigid-Body Model of Large-Deflection Compliant Mechanisms
,”
ASME J. Mech. Des.
,
118
(
1
), pp.
126
131
.10.1115/1.2826843
53.
Belfiore
,
N. P.
,
2014
, “
Functional Synthesis of a New Class of Micro Electro-Mechanical Systems
,”
Advances in Soft Computing, Intelligent Robotics and Control
. Vol. 8 (Topics in Intelligent Engineering and Informatics),
Springer International Publishing
, pp.
81
93
.
54.
Freudenstein
,
F.
,
Bottema
,
O.
, and
Koetsier
,
M.
,
1969
, “
Finite Conic-Section Burmester Theory
,”
J. Mech.
,
4
(
4
), pp.
359
373
.10.1016/0022-2569(69)90016-0
55.
Belfiore
,
N. P.
,
Prosperi
,
G.
, and
Crescenzi
,
R.
,
2014
, “
A Simple Application of Conjugate Profile Theory to the Development of a Silicon Micro Tribometer
,”
Proceedings of ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis
, ASME, Copenhagen, Denmark, July 25–27.
56.
Balucani
,
M.
,
Belfiore
,
N. P.
,
Crescenzi
,
R.
, and
Verotti
,
M.
,
2011
, “
The Development of a MEMS/NEMS-Based 3 D.O.F. Compliant Micro Robot
,”
Int. J. Mech. Control
,
12
(
1
), pp.
3
10
.
57.
Chang
,
S.-L.
, and
Tsai
,
L.-W.
,
1990
, “
On the Redundant - Drive Backlash - Free Robotic Mechanisms
,”
ASME J. Mech. Des.
115
(2), pp. 247–254.
58.
Nemeth
,
N.
,
Evans
,
L.
,
Jadaan
,
O.
,
Sharpe
,
W.
,
Beheim
,
G.
, and
Trapp
,
M.
,
2007
, “
Fabrication and Probabilistic Fracture Strength Prediction of High-Aspect-Ratio Single Crystal Silicon Carbide Microspecimens With Stress Concentration
,”
Thin Solid Films
,
515
(
6
), pp.
3283
3290
.10.1016/j.tsf.2006.01.041
59.
Merlijn Van Spengen
,
W.
,
2012
, “
Static Crack Growth and Fatigue Modeling for Silicon MEMS
,”
Sens. Actuators, A
,
183
, pp.
57
68
.10.1016/j.sna.2012.05.042
You do not currently have access to this content.